Geometrical construction of quantum groups representations

We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2,\text{BbbC})▹{\text{BbbC}}^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces of polynomial functions with a quadratic relations.